Aysenur  Ocalan, Ozkan Ocalan, and Umut Mutlu Ozkan
Oscillatory Behavior For Nonlinear Delay Difference Equation With Non-Monotone Arguments
Dynamic Systems and Applications 31 (2021) 53-62

https://doi.org/10.46719/dsa202231.01.04

ABSTRACT.
The aim of this paper is to obtain the some new oscillatory conditions for all solutions of nonlinear difference equation

(⋆) Δx(n) + Σ p_i(n)f_i(x (τ_i (n))) = 0, n = 0, 1, …. ,

where, for i = 1, 2, …. , m, (p_i(n)) are sequences of nonnegative real numbers and (τ_i (n)) are not
necessarily monotone sequences, f_{i Ɛ} C(R;R) and xf_i (x) > 0 (i = 1, 2, … , m) for x _≠ 0:

AMS (MOS) Subject Classification. 39A10, 39A21.
Key Words and Phrases. Delay difference equation, non-monotone arguments, nonlinear, oscillation.